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Find the general solution. 2. Find the general solution. X' = AX A= 1 1 0...
(25 PTS) 2. Find the general solution of x' = AX, where A = A = [5 -- }], x(0) = 1
z(t) y(t) 2 0 (22 points) Find the general solution to3"(1)-Ax(t), where A = | 1-2 | , and i(t)-
1. Find a general solution of X" = AX with -5 4 (1) A= (2) A= 4 -5 2 3 1 -2 4 (3) A= 2 2 3 -3 (4) A= -6 2 4
Use the variation of parameters formula to find a general solution of the system x'(0) AX(t) + f(t), where A and f(t) are given -4 2 А. FU) 21 12 +21 Let x(t) = xy()+ X(t), where x, (t) is the general solution corresponding to the homogeneous system, and X(t) is a particular solution to the nonhomogeneous system. Find X. (t) and X.(1).
Find the general solution to the system of linear differential equations X'=AX. The independent variable is t. The eigenvalues and the corresponding eigenvectors are provided for you. x1' = 12x1 - 8x2 x2 = -4X1 + 8x2 The eigenvalues are 11 = 16 and 12 = 4 . The corresponding eigenvectors are: K1 = K2= Step 1. Find the nonsingular matrix P that diagonalizes A, and find the diagonal matrix D: p = 11 Step 2. Find the general solution...
Please help me solve this, thanks! Find the general solution to the system x' = Ax where A is the given matrix. | -2 -2 -6 A= 0 0 6 | 0 -2 -8 b) X(t)=( X(t)= Ce 0 e) X(t)= C, e 20 +46?' -6 +2° -1 | 2 f) None of the above. Find the general solution to the system x'= Ax where A is the given matrix. 0 1 0 A= 0 0 1 | -20 16...
3. Find a general solution of the system X' = AX with 3 0 0 -3 4 (1) A (2) A = 0 2 0 (3) A 6 -5 4 0 1 -3 0 3 -5 0 5 0 0 -1 1 (4) A [1 7 4 -5 3 (5) A = 3 -5 -3 5 5 -1 3 (6) A 1 0 0 0 2 2 0 0 0 3 3 0 0 0 4 4
2. Find a general solution of X' = AX if 3 -1 (1A A1 = 12 = 2 1 [ 1] 3 -1 (2) A= 1 Xi = 1; 12 = 13 = 2 1 (3) A = 1 Xi = 0; 12 = 13 = 5 1 (4) A= 5 -4 0 0 2 0 2 5 0 0 0 3 1 0-1 1 1 0 0 2 2 - 1 0 1 0 11 = 1; 12 =...
4. (a) (8 points) Find the general solution of x' = Ax, for A= 2. Write the solution in vector form. 1-1 -3 (b) (4 points) Using your vector solution, write a matrix solution X(t). (c) (4 points) Using the matrix solution from part (b), determine en
Find the general solution of the system x' = Ax where A is the given matrix. If an initial condition is given, also find the solution that satisfies the condition. 1.1 5 2 :| -2 1 )